Final Report Essentials

Author
Affiliation

Jeremy Springman

University of Pennsylvania

Published

April 12, 2025

Index Variables

Simple Additive Index

  • Measured on the same scale
  • Share direction

Adding numberical measures

Count of times a respondent…

  • q13_4_1: Contacted gov’t official
  • q13_6_1: Contacted a student representative
  • q13_7_1: Contacted an NGO
  [1]  0  3  1  0  1  5  1  4  0  1  2 10  0  2  0  3  4  0  3  1  2  1  0  5  1
 [26]  0  7  6 10  4  0  1  2  4  0  0  3  0  4  1  0  0  0  0  0  1  0  1  1  4
 [51]  4  0  0  3  0  4  3  1  1  0  4  8  0  0 11  5  1  0  0  1  0  0  0  0  1
 [76]  1  1  3  4  1  3  3  2  1  5  1  7  0  0  2  0  2  6  1  0  2  1  4  0  2
[101]  1  0  3  2  2  0  1  0  0  1  2  5  0  4  1  2  0  1  0  0  2  0  7  2  7
[126]  3  0  0  6  0  2  2  0  0  6  0  0  0  5  1 17  2  9  1  1  2  0  2  1  1
[151] 13  0  0  2  1 14  0  1  8  0  1  0  0  9  1  0  6  5  1  0  4  2  0  0  3
[176]  3  3  0  1  0  1  0  0  0  2  5  2  0  5  4  2  2  1  2  1  0  0  0  1  1
[201]  0  4 18  3  0  1  1  0  1  0  7 17  2  0  2  0  3  2  0  1  1  0  0  9  0
[226]  0  1  0  1  0  1  2  0  1  2  1  2  6  0  0  1  0  1  2  4  0  1  0  7  0
[251]  3  1  0  1  3 20  0  2  4  2  0  0  3  0  1  0  2  1  0  0  8 14  2  7  0
[276]  0  0  3  0  2  5  4  5  0  0  2  5  0  2  0  3  0  0 10  1  1  3  9  1  0
[301]  6  1  0  2  2  2  0  0  7  6  2  8  2  0  5 13  1  1  2  0  1  0  4  3  0
[326]  0  0  1  1  3  1  1  0  3  0  0  7 12  0  0  2  1  6  6  1  0  0 10  1  0
[351]  4  0  5  5  1  1  0  6  5  0  0  1  0  0  1  2  4  2  2  0  3  0  3  5  5
[376]  4  0  0 17  6  0  0  0  5  5  0 13  0  2  1  0  3 11  1  0  2  2  1  0  0
[401]  1  1  5  2  0  0  3  0  3  0  0  2  1  4  0  0  3  1  3  3  0  0  0  2  0
[426]  1  3  5  7  5  0  0  0 11  5  0  3  1  2  0  1  1  0  3  0  1  1  0  0  3
[451]  0  6  2  0  3  5  1  0  0  4  0  7  1  2  1  3  1  3  0  2  4  0  1  2  0
[476]  3  5  5  1  0  0  0  0  5  0  0  1  0  0  1  0  1 13  6  0  0  0  2  0  5
[501]  2  1  5  1  1  2  0  0  8  0  0  0  0  1  0  3  4  1  2  0  0  5  0 30  1
[526]  2  2  4  2  0  0  7  0  2  2  3  0  0  3  0  0  0  1  1  1  6  5  1  2  0
[551]  1  0  6  0  0  0  5  2  0  0  0  0  2  0  0  5  3  3  1  2 10  5  0  3  5
[576]  4  1  2  2  0  2  0  2  0  1  2  0  8  4 15  1 13  2  1  3  4  1  0  2  0
[601]  8  3  3  0  4  0  0  0  1  1  5  0  1  9  0  0  2  1  1  3  0  3  0  1  4
[626]  2  0  0  1  4  7  3  2 13  0  0  1  1  0  2  0 13  0  0  0  2  0  0  0  1
[651]  0  1  1  2  1  4  0  4  0  0  3  1  7  4  4  0  2  0  3  3  2  1  0  4  0
[676]  9  9  2  0  3  2  0 11  1  0  7  0  0  0  3 18  3  1  0  1  2  2  1  3  0
[701]  5  1  6  2  2  1  6  0  0  4  0  0  0  2  0  3  3 12  5  0  0  8  1  4  1
[726]  0  6  0  1  1  0  0  0  2  0  0  0  3  2  3  0  1  2  1  0  3  0  3  0  1
[751] 10  2  2  3  0  0  1  3  0  2  8  5  0  0  2  3  4  1  3  0  0  0  3  3  0
[776]  6  0  0  1 14  4  3  2  2  0  0  8  3 32  3  2  0  2  2  0  0  0  2  9  0
[801]  2  1  3  0  0  2  5  2  0  0  3  5  0  3  1  0  6  0  3  3  0  0  2  3  0

Do they ‘hang together’?

[1] 0.4910388

Visualizing the result

Thinking about weights

Stretching the concept…

What if we wanted to add the count of times a respondent…

  • q13_5_1: Signed a petition
[1] 0.6121334

Adding likert measures

  • q16_1: Intention to join religious group
  • q16_2: Intention to join ethnic interest group
  • q16_3: Intention to join political party
  • q16_4: Intention to join voluntary org

Averaged Z-Scores

  • \(Z = (X - \mu) / \sigma\)
  • \(z_i = \frac{X_i - \bar{X}}{s}\)
  • Standardized: Mean of 0 and standard deviation of 1

Interaction Terms

Differences across groups

Binary


  Year I  Year II Year III 
     327      277      221 

  0   1 
327 221 
Multivariate Interaction
(Intercept) −0.14** (0.05) −0.18** (0.06)
moved 0.27*** (0.06) 0.33*** (0.07)
year −0.05 (0.05) 0.04 (0.09)
moved × year −0.14 (0.11)
Num.Obs. 534 534
R2 Adj. 0.045 0.046

Continuous-ish


  0   1   2 
327 277 221 
Bivariate Multivariate Interaction
(Intercept) −0.150*** (0.036) −0.121** (0.045) −0.169** (0.056)
moved 0.234*** (0.045) 0.228*** (0.045) 0.301*** (0.067)
year −0.029 (0.027) 0.019 (0.042)
moved × year −0.080 (0.054)
Num.Obs. 809 809 809
R2 Adj. 0.032 0.032 0.033

More complex


  0   1   2 
327 277 221 
Bivariate Multivariate Interaction
(Intercept) −0.150*** (0.036) −0.114* (0.046) −0.184** (0.060)
moved 0.234*** (0.045) 0.232*** (0.045) 0.334*** (0.072)
year2 −0.060 (0.049) 0.077 (0.092)
year3 −0.053 (0.054) 0.038 (0.085)
moved × year2 −0.194+ (0.109)
moved × year3 −0.142 (0.110)
Num.Obs. 809 809 809
R2 Adj. 0.032 0.031 0.033

Differences over time

Cross-Sectional

Bivariate Multivariate Interaction
(Intercept) −0.179*** (0.023) −0.165*** (0.027) −0.150*** (0.033)
moved 0.257*** (0.029) 0.257*** (0.029) 0.234*** (0.041)
time −0.027 (0.027) −0.058 (0.047)
moved × time 0.046 (0.057)
Num.Obs. 1625 1625 1625
R2 Adj. 0.047 0.047 0.047

Fixed Effects

Simple Fixed Effects Interaction
(Intercept) 0.005 (0.020) −0.319** (0.115) −0.294* (0.115)
time −0.027 (0.028) −0.028*** (0.008) −0.059*** (0.014)
moved −0.033 (0.162)
moved × time 0.047** (0.017)
Num.Obs. 1625 1625 1625
R2 Adj. 0.000 0.916 0.917